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Description of  Krishna's BSc. Obj. Complex Analysis, Edition-1

SYLLABUS- B.Sc. OBJ. COMPLEX ANALYSIS, Unit 1 Functions of a complex variable, Concepts of limit, continuity and differentiability of complex functions, Analytic functions, Cauchy-Riemann equations (Cartesian and polar form), Harmonic functions, Orthogonal system, Power series as an analytic function. Unit 2 Elementary functions, Mapping by elementary functions, Linear and bilinear transformations, Fixed points, Cross ratio, Inverse points and critical points, Conformal transformations. Unit 3 Complex Integration, Line integral, Cauchy’s fundamental theorem, Cauchy’s integral formula, Morera’s theorem, Liouville theorem, Maximum Modulus theorem, Taylor and Laurent series. Unit 4 Singularities and zeros of an analytic function, Rouche’s theorem, Fundamental theorem of algebra, Analytic continuation. Unit 5 Residue theorem and its applications to the evaluation of definite integrals, Argument principle.